I need help;
Sam has 4 2/3 of a cake at a party. He wants to distrubute the cake such that each child gets 1 1/6 of a whole cake. how many children can he distrubute the cake to?
It’s okay if you don’t ans the full question just help me out a bit.
If there are x children, then you need
(1 1/6)x = 4 2/3
7/6 x = 28/6
...
Can someone please lead me to the right direction in answering it , thanks. :)
-gummy
Tysm
Sure! To solve this problem, we need to find out how many times the amount of cake each child gets (1 1/6) fits into the total amount of cake Sam has (4 2/3).
To compare the fractions effectively, we first need to convert the mixed numbers into improper fractions.
For 4 2/3, we can multiply the whole number (4) by the denominator of the fraction (3) and then add the numerator (2) to get the new numerator (14). The new fraction is (14/3).
For 1 1/6, we can calculate (1 * 6 = 6), then add the numerator (1) to get the new numerator (7). The new fraction is (7/6).
Now, we can divide the total amount of cake Sam has (14/3) by the amount each child gets (7/6).
Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction. So, we can calculate:
(14/3) / (7/6) = (14/3) * (6/7)
To multiply fractions, we simply multiply the numerators to get the new numerator (84), and multiply the denominators to get the new denominator (21).
So, (14/3) * (6/7) = 84/21
Now, we can simplify the resulting fraction. Both the numerator and denominator are divisible by 3:
84/21 = (84 ÷ 3) / (21 ÷ 3) = 28/7
Finally, we can simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 7:
28/7 = (28 ÷ 7) / (7 ÷ 7) = 4/1 = 4
Therefore, Sam can distribute the cake to 4 children, with each child receiving 1 1/6 of a whole cake.